PIE-Phase Diagram Experiments

These activities are for sophomore or junior students in geology. It can, for instance, be part of a core-curriculum class (200/2000 level) for a geology degree.
The demonstration (1) and the lab activity (2) do not require prior knowledge on phase diagram.
The written assignment (3) can be used as an assessment at the end of the module on binary phase diagram with a simple eutectic.

In class demonstration (1) and lab activity (2) require no prior knowledge on phase diagram or Excel. These activities can be used as a first introduction to eutectic binary phase diagrams.
The written assessment (3) requires to understand how to read and interpret a phase diagram. This assessment can be used as a final exercise or exam at the end of a module on binary phase diagram.

Each activity can be used as stand-alone activity.
Alternatively, the instructor can choose to use all three with the in-class demonstration serving as an introduction to the lab activity. (We would not recommend doing the demonstration during the lab period however as the students will need the 3-hour lab period to complete the lab activity). The final written assignment is also related to the in class demonstration.

(1) The goal of the short in-class demonstration is to introduce, for the first time, the concept and application of eutectic materials to students who have never worked with phase diagrams in multi-component systems.

(2) During the lab activity, the students will build their own phase diagram. The goal of this activity is for students:
-To understand how phase diagrams are built
-To understand the concepts of liquidus surface and solidus temperature
-To learn how to estimate experimental uncertainty

(3) The written exercise is to assess if students can read and interpret data from a binary phase diagram.

The in-class demonstration involves:
- Data collection
- Formulation of hypotheses

The lab activity involves:
- Understand the concept of liquidus surface and solidus temperature
- Analysis of data
- Assessment of experimental uncertainty
- Formulation of hypothesis

The written exercise involves:
- Examine the students' general knowledge of the principles of binary phase diagrams
- Test students' confidence in reading the topology and measurable quantities reported in a phase diagram
- Challenge students' understanding of the role of phase diagrams and their applications of daily examples (such as computer technology).

The lab activity also involves:
- Working in groups
- Hands-on activity
- Collecting experimental data
- Use of Excel

(1) In class demonstration. By putting in contact a piece of gallium and a piece of indium that were previously weighted, the eutectic temperature of the Ga-In system is reached. Students will be able to visualize the formation of melt. At that point, the instructor can initiate an in-class discussion on what the students think happened and which metal is likely melting during this reaction. The liquid is wiped off and the two pieces of metal are weighted again. Students can then perform prompt mass balance calculations to estimate the proportion of each metal that was consumed. The same exercise is repeated, but this time with a large piece of indium. At the end of the demonstration, students must start formulating hypotheses on why the two tests resulted in same/similar results.

(2) In Lab activity: students work with various proportions of Lauric and Mauric acids to estimate the liquidus and solidus temperature of the mixtures. Students work in small groups (2 or 3). Each group is given 3 mixtures. Data from all students are then compiled and distributed to the class and students must then compare their experimental data with data published in the literature.

(3) Written exercise: students work individually on a problem set that uses the Ga-In binary system. They must demonstrate that they know how to read a phase diagram with a simple eutectic. This exercise also serves as an introduction to multi-component system by introducing a 3rd component in the discussion.

In class demonstration (Acrobat (PDF) 338kB Apr8 25)
Lab activity - Student handout (Microsoft Word 2007 (.docx) 28kB Apr8 25) 
PIE-Part 1 (Excel 2007 (.xlsx) 16kB Apr8 25) 
PIE-Part 2 (Excel 2007 (.xlsx) 16kB Apr8 25) 
PIE-written assignment (Microsoft Word 2007 (.docx) 1.5MB Apr8 25)

Keys_for_lab_activity.xlsx -- educator-only file

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PIE-written_assignment_keys.pdf -- educator-only file

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For the class demonstration, the results might not be perfect given the empirical nature of the assignment. The idea is not to try to exactly reproduce the eutectic of the Ga-In binary system but to show that independently of the mass of the two components, similar proportion of Ga and In are consumed during the reaction. The experiment can be a bit messy, so it's preferable to wear a lab coat and gloves and to place paper towel on the table, but it is not toxic and easy to clean.

For the lab activity, we recommend preparing all the mixtures in advance to make sure the students have time to properly make their measurements and to complete the lab in a 3-hour period. The instructor can make a short demonstration at the beginning of the lab on how these mixtures were prepared (see teacher notes below). This usually results in a better quality of the data. Once prepared and melted completely once, the mixtures can be stored and reused for future sessions of the same lab. For convenience, we provided results acquired on three different sessions (Fall 2023, Spring 2024, and Fall 2024). We recommend compiling data in the same spreadsheet session after session, so students can discuss assessment and experimental error.

1) After the Ga-In in class demonstration, the student should understand that the initial melting point does not depend on the fraction of each component in the system and stays constant.

2) Rubrics are provided for the lab activity:

full credits points earned
part 1 (group work) 90 
1. starting material preparation 5 weight calculations were performed correctly
21a. TL measurements 30 10 point each -1 for each 5 degrees off 
21b: justification for TL best choice 10 justification is scientifically sound. 
22a. T vs time measurement 20 curve is plotted correctly, the graph axes are named, the instructions for measurement were followed.
Inflection point can be seen
22b. Estimation of Ts 15 1 point off for each 2 degrees off 
22c. Justification of uncertainty on TS 5 justification is scientifically sound. 
3. Experimental results 5 results are reported in Table 5

part 2 (individual work) 50 
1. plotting theoretical data 20 axes are labelled correctly and with the correct scale. 
2. Conversion in molar fraction 5 calculations are done correctly 
3. Plot expet data on the same graph 10 correct use of series in excel. Plot both experimental TS and TL
4a. TL vs X 3 correct description with min TL at 0.65LA 
4b. Estimate TS 3 observation than minimum TL is also the freezing (solidus) temperature, aka the eutectic temperature. 
1 point off every degree off
5ai. Origin of large errors 3 justification is scientifically sound 
5aii. Origin of small errors 3 justification is scientifically sound 
5b experimental vs theoretical TS 3 comparison between TS is discussed. Outlier(s), if present, are discussed

3) Students have successfully met the goals of the written assignment if they answer the problem set thoroughly and accurately. See appended copy of the assignment and its copy listing the keys to the proposed questions.

Zhixuan Fan, Yunchao Zhao, Xuying Liu, Yu Shi, and Dahua Jiang (2022), Thermal Properties and Reliabilities of Lauric Acid-Based Binary Eutectic Fatty Acid as a Phase Change Material for Building Energy Conservation. ACS Omega 2022 7 (18), 16097-16108, DOI: 10.1021/acsomega.2c01420ences

Bjorn Joos, Marlies K. Van Bael, and An T. Hardy (2020), Construction of a Room-Temperature Eutectic Binary Phase Diagram by Use of Differential Scanning Calorimetry, Journal of Chemical Education 2020 97 (8), 2265-2272, DOI: 10.1021/acs.jchemed.0c00204

Bridget C. Rugg, and Tim G. Chart (1990), A critical assessment of thermodynamic and phase diagram data for the gallium-indium system. Calphad, 14(2), 115-123, DOI: 10.1016/0364-5916(90)90013-P.

John's Brady interactive textbook: https://www.science.smith.edu/~jbrady/petrology/igrocks-diagrams/binary/binary-list.php
Provide practicals to learn and practice on how to read phase diagrams.